1. Open Outlook Web Access (OWA) HERE.

2. Log in using your email credentials. (Note: have your cell phone ready as you will be asked to enter a 2FA code to log in)

3. After logging in, click the gear icon > Options > General > My account

4. Your current mailbox size is shown in the lower-right corner. 

Refresh this page after deleting old emails to see if your mailbox size is reducing.